E 6 unification model building. III. Clebsch–Gordan coefficients in E6 tensor products of the 27 with higher dimensional representations

Abstract

E 6 is an attractive group for unification model building. However, the complexity of a rank 6 group makes it nontrivial to write down the structure of higher dimensional operators in an E6 theory in terms of the states labeled by quantum numbers of the standard model gauge group. In this paper, we show the results of our computation of the Clebsch–Gordan coefficients for the products of the 27 with irreducible representations of higher dimensionality: 78, 351, 351′, 351¯, and 351¯′. Application of these results to E6 model building involving higher dimensional operators is straightforward.